Solve the system of linear equations for x and y:
`x+y=15`
`3x-2y=-5`

Options

A. 6, 12
B. 8, 16
C. 5, 10
D. 7, 14

Answer

To solve the system of linear equations:

1. **Write down the equations:**
\[ x + y = 15 \quad \text{(1)} \]
\[ 3x - 2y = -5 \quad \text{(2)} \]

2. **Rearrange equation (1) to express y in terms of x:**
\[ y = 15 - x \quad \text{(3)} \]

3. **Substitute equation (3) into equation (2):**
Replace \(y\) in equation (2) with \(15 - x\):
\[ 3x - 2(15 - x) = -5 \]

4. **Simplify the equation:**
\[ 3x - 30 + 2x = -5 \]
Combine like terms:
\[ 5x - 30 = -5 \]

5. **Add 30 to both sides:**
\[ 5x = 25 \]

6. **Divide by 5 to solve for x:**
\[ x = 5 \]

7. **Substitute the value of x back into equation (3) to find y:**
\[ y = 15 - 5 = 10 \]

8. **Final solution:**
\[ x = 5, \quad y = 10 \]

Thus, the solution to the system of equations is \(x = 5\) and \(y = 10\).